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Monthly Archives: March 2013

A while ago (a long while ago, I guess — hey, I have a job, so I’m busy), I posted about how 19-tone equal temperament is a diatonic tuning.  But is it the only one?  Other than 12-TET, that is?

Obviously not.  Let’s take a look at how it works!

Under our harmonic system, we base everything on the fifth.  A perfect fifth is a frequency ratio of exactly 1.5, which translates to about 701.955 cents.  Our 12-TET scale only uses multiples of 100 cents, so it approximates the perfect fifth quite well at 700 cents.  This is far from the only possible value, however!  There’s a small range where we can arbitrarily choose our fifth, and that’s what we’re about to explore.

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